Let us mention that in [1]}, [2]} and [3]} the MOP are expressed in terms of Schur complements that play the role of determinants in the standard scalar case. In [3]} an study of matrix Szegő polynomials and the relation with a non Abelian Ablowitz–Ladik lattice is carried out, and in [5]} the CMV ordering is applied to study orthogonal Laurent polynomials in the circle.
